 | Euclid, Dionysius Lardner - 1828 - Liczba stron: 542
...Propositions are introduced by SIMSON. PROPOSITION A. THEOREM. (480) If the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then, if the first be greater than the second, the third is also greater than the fourth ; and if... | |
 | Euclid, Robert Simson - 1829 - Liczba stron: 548
...relation of two magnitudes of the same kind to one another, in respect of quantity.'* IV. Magnitudes arc said to have a ratio to one another, when the less...four magnitudes is said to have the same ratio to the scoond, which the third has to the fourth, when any equimultiples whatsoever of the first and third... | |
 | Pierce Morton - 1830 - Liczba stron: 584
...having the same ratio to two others В and D, of the same kind with the former two respectively. Def. 7. The first of four magnitudes is said to have the same ratio to the se* By the word " corresponding" here used, it U R«TÍy iat«*nded to point out the fact of there... | |
 | Euclid - 1833 - Liczba stron: 216
...ought to be defined, is still a subject of controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth being taken, the equi-multiples of the first... | |
 | Robert Simson - 1835 - Liczba stron: 544
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
 | Euclid - 1835 - Liczba stron: 540
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
 | 1835 - Liczba stron: 684
...equal to, or less than the corresponding magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* • "The first of four magnitudes is said to have the same ratio tu the second, which the third has to the fourth, when any equimultiples whatsoever of the first and... | |
 | 1836 - Liczba stron: 488
...oft as there are units in the product of these two numbers. IV. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be tcriken of the first and third, and any whatever of the second... | |
 | William Whewell - 1837 - Liczba stron: 226
...GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same...second which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of... | |
 | Euclid, James Thomson - 1837 - Liczba stron: 410
...the sixth, is of the fourth D. If, therefore, &c. PROP. IV. THEOR. IF the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any like multiples whatever of the first and third have the same ratio to any like multiples... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
